I, too, found myself looking between engineering and teaching mathematics
when I was in college. I have never regretted my choice to become a part of
the mathematics education world. A friend of mine did the same thing and
has never regretted her choice to become an engineer.
I think it's great that you are exploring your options. Now for your
questions...
Do you have to teach in North Dakota?
No. There is a severe shortage of qualified mathematics teachers all
over the country.
However, to teach in another state, you must meet the credential
requirements of the state in which you wish to teach. The education
department at NDSU is a good place to start researching this information.
If you are interested in teaching in California (yes, I teach in
California), I suggest you contact the Commission on Teacher Credentialling
to see what is required. Their web address is http://www.ctc.ca.gov.
Could you return to school later and get a teaching credential?
Absolutely. The physics teacher at my school is was a nuclear engineer
for 20 years before he got his teaching credential. He doesn't make half as
much money as he used to. BUT he loves what he is doing and his students
think the world of him.
Hope this helps!
-Jeanne, for the Teacher2Teacher service